In this study, some shrinkage estimators using a median ranked set sample in the presence of multicollinearity were studied. Initially, we constructed the multiple regression model using median ranked set sampling. We also adapted the Ridge and Liu-type estimators to these multiple regression model. To investigate the efficiency of these estimators, a simulation study was performed for a different number of explanatory variables, sample sizes, correlation coefficients, and error variances in perfect and imperfect ranking cases. In addition, these estimators were compared with other estimators that are based on ranked set sample using simulation study. It is shown that when the collinearity is moderate, Ridge estimator using median ranked set sample performs better than other estimators and when the collinearity increases, Liu-type estimator using median ranked set sample gets better than all other estimators do. When the collinearity is smaller than 0.95, ridge estimator based on median ranked set sample is more efficient than Liu-type estimator based on same sample. However, this threshold increases as the sample size increases and the number of explanatory variables decreases. In addition, real data example is presented to illustrate how collinearity affects the estimators under median ranked set sampling and ranked set sampling.

在这项研究中，研究了一些在存在多重共线性的情况下使用中位排序集样本的收缩估计量。最初，我们使用中位数排序集抽样构建了多元回归模型。我们还将 Ridge 和 Liu 型估计量调整到这些多元回归模型。为了研究这些估计器的效率，对完美和不完美排名案例中不同数量的解释变量、样本量、相关系数和误差方差进行了模拟研究。此外，这些估计量与其他基于使用模拟研究的排序集样本的估计量进行了比较。结果表明，当共线性适中时，使用中位数排序集样本的 Ridge 估计器的性能优于其他估计器，并且当共线性增加时，使用中位数排序集样本的 Liu 型估计器比所有其他估计器都好。当共线性小于0.95时，基于中位数排序集样本的岭估计比基于相同样本的刘型估计更有效。然而，这个阈值随着样本量的增加和解释变量的数量的减少而增加。此外，还给出了真实数据示例来说明共线性如何影响中位数排序集抽样和排序集抽样下的估计量。